Comparing decisional maps

Among the many interesting decision problems raised by the use of geographic information systems, we address that of comparing maps representing the state of a given region at different stages of an evolution. We assume that the maps representing the state of the region are all partitioned in the same system of zones. Each zone is assessed on a discrete ordinal scale; the state of the region is reflected by such an assessment of all its zones. We analyze two models of preference on a set of maps of a region. The first only takes into account the frequency distribution of the zones of the region that belong to the various categories of the ordinal assessment scale. This model is directly inspired by the expected utility model in decision under risk. Our second model takes into account not only the distribution of the zones but also one aspect of their geographic location, namely contiguity of the zones belonging to the same category. For both models, we develop procedures for eliciting the model's parameters.